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MOTION                                       91
It must be remembered that dv is the vector difference of the velocities at the beginning and at the end of the interval of time dt] therefore f is a vector magnitude with a direction which is, in general, different from that of the velocity.
87.   Dimensions and Units of Acceleration.  The dimensions of acceleration are [LT~~2].   The unit of acceleration is a unit change in the velocity per second.    Therefore the
C.G.S. unit is  ----- or ----'-.   Thus if the velocity of a
sec.          sec.~
particle increases by an amount of one - during each
second it has a unit acceleration. The engineering unit of acceleration is the foot per sec. per sec., '
1.   Express the engineering unit of acceleration in terms of the C.G.S. unit.
2.   Taking the value of the gravitational acceleration to be 980 -^^ >
fi   ,..      ,     .     ft.       , miles                                                     sec-
find its value in----- and - 
sec.2         hr.2
3.   A train moving at the rate of 30 kilometers per hour is brought to rest in two minutes.   Find the average acceleration and express it in
,          - cm.     ft.       j km.
terms of----- >----- and -- 
sec.2   sec.2        hr.2
88.   Components of Acceleration along Rectangular Axes. 
Suppose a particle*to describe a path in the xy-plane. Then if YI and v2 be the velocities at two neighboring points, we can write
= (x2 + 2)  (xi + yi) = dx+dy. x _ dv = dx     dy dt     dt     dt
But since                      f = f * + f y,
r        ,     x     _   dX.1     li
dt     dt